📘 PAPER 3 – ARTIFICIAL INTELLIGENCE & ROBOTICS UNIT 2: KNOWLEDGE REPRESENTATION & REASONING (university of allahabad)

 

🔴 UNIT 2: KNOWLEDGE REPRESENTATION & REASONING

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1️⃣ Knowledge Representation (KR)

✅ Definition

Knowledge Representation is the method used to store knowledge in a machine so that it can:

• Reason

• Learn

• Make decisions

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✅ Goals of Knowledge Representation

✔ Represent real-world information
✔ Enable reasoning
✔ Easy to modify
✔ Efficient retrieval

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2️⃣ Propositional Logic

✅ Definition

Propositional Logic is a formal system in which:

• Statements are either True or False

• Uses logical connectives

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🔹 Basic Elements

Propositions

Statements that have truth values.

Example:

• “Ram is tall” → True/False

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Logical Connectives

Symbol	Meaning
¬	NOT
∧	AND
∨	OR
→	IMPLIES
↔	IFF

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Example:

P: It is raining  
Q: I carry umbrella  

P → Q

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3️⃣ Syntax and Semantics

Syntax

Rules for forming valid expressions.

Semantics

Meaning or truth value of expressions.

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4️⃣ Inference in Propositional Logic

🔹 Reasoning Methods

1. Forward Chaining

• Data-driven

• Starts from facts

• Moves forward using rules

2. Backward Chaining

• Goal-driven

• Starts from goal

• Works backward

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5️⃣ Resolution Principle

Definition:

Resolution is a rule of inference used for proving statements.

Example:

P ∨ Q  
¬Q  
---------
P

✔ Used in theorem proving
✔ Important exam topic

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6️⃣ First Order Logic (FOL)

✅ Definition

First Order Logic is more powerful than propositional logic because it:

• Uses quantifiers

• Represents objects and relationships

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🔹 Quantifiers

Symbol	Meaning
∀	For all
∃	There exists

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Example:

∀x (Human(x) → Mortal(x))

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7️⃣ Inference in First Order Logic

🔹 Unification

Process of making two expressions identical.

Example:

P(x) and P(Ram)
⇒ x = Ram

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🔹 Resolution in FOL

Steps:

1. Convert to clause form

2. Skolemization

3. Apply resolution rule

4. Derive empty clause

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8️⃣ Knowledge Representation Techniques

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🔹 1. Semantic Networks

Graph-based representation:

• Nodes → Objects

• Arcs → Relationships

Example:

Bird → can fly  
Sparrow → Bird

✔ Easy to understand
❌ Limited reasoning power

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🔹 2. Frames

Structured representation using slots and values.

Example:

Slot	Value
Name	Bird
Wings	Yes
Fly	Yes

✔ Used in expert systems

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🔹 3. Conceptual Graphs

• Graphical form of logic

• Combines semantic nets + logic

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9️⃣ Uncertain Knowledge

Problem:

Real-world information is often:

• Incomplete

• Uncertain

• Imprecise

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🔹 Probabilistic Reasoning

Uses probability to represent uncertainty.

Example:
P(Rain) = 0.7

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🔹 Fuzzy Logic

Definition:

Fuzzy logic allows partial truth values between 0 and 1.

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Example:

Temperature	Truth Value
Cold	0.2
Warm	0.7
Hot	0.9

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Advantages:

✔ Handles uncertainty
✔ Used in washing machines, ACs
✔ Human-like reasoning

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🔟 Learning in AI

Types of Learning:

🔹 1. Supervised Learning

• Uses labeled data

• Example: Classification

🔹 2. Unsupervised Learning

• No labeled data

• Clustering

🔹 3. Reinforcement Learning

• Reward-based learning

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1️⃣1️⃣ Concept Learning

Learning general concepts from examples.

Example:
Learning “Bird” from examples like sparrow, pigeon.

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1️⃣2️⃣ Inductive Learning

Learning by:

• Observing examples

• Generalizing rules

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1️⃣3️⃣ Decision Tree Learning

Steps:

1. Select attribute

2. Split data

3. Build tree

4. Predict output

✔ Simple
✔ Easy to understand

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1️⃣4️⃣ Neural Networks (Intro)

Definition:

A Neural Network is inspired by the human brain.

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Single Layer Neural Network

• Input layer

• Output layer

• Weighted connections

Used for:

• Classification

• Pattern recognition